Using Kepler's third law, determine the period

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Homework Help Overview

The discussion revolves around applying Kepler's third law to determine the orbital period of a hypothetical planet located three times farther from the Sun than Earth. The problem assumes a circular orbit and involves understanding the implications of the law in relation to mass and distance.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the application of Kepler's third law, questioning the calculations leading to the orbital period of 5.2 years. There is a focus on identifying errors in mathematical reasoning and clarifying the implications of mass independence in the context of the law.

Discussion Status

Some participants have identified errors in their calculations and are seeking clarification on the implications of mass in relation to Kepler's laws. The discussion is productive, with participants questioning assumptions and exploring the conceptual framework of the law.

Contextual Notes

There is a noted assumption that the masses of the planets are negligible compared to the Sun, which is central to the application of Kepler's laws. This assumption is being examined in light of hypothetical scenarios involving massive objects.

Calpalned
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Homework Statement


If there were a planet three times farther from the sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun? Assume the orbit is a circle.

Homework Equations


Kepler's 3rd Law ##= (\frac{r_1}{r_2})^3 = (\frac{T_1}{T_2})^2 ##

The Attempt at a Solution


##= (\frac{3r_E}{r_E})^3 = (\frac{T}{1})^2 ##
T = 3 years Correct answer: T = 5.2 years
Where is my blunder? Thank you all so much.
 
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Calpalned said:

The Attempt at a Solution


##= (\frac{3r_E}{r_E})^3 = (\frac{T}{1})^2 ##
T = 3 years Correct answer: T = 5.2 years
Where is my blunder? Thank you all so much.
Show the math one step at a time.
 
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gneill said:
Show the math one step at a time.
I just found out my error. ##3^3 = 27##. I accidentally wrote 9 instead of 27.
Thanks for helping Gniell
 
I have one more question...
Part B of this question asks if I can use the data to solve for the mass of the hypothetical planet. The answer is no. "No mass data can be calculated from this relationship, because the relationship is mass- independent. Any object at the orbit radius of 3 times the Earth’s orbit radius would have a period of 5.2 years, regardless of its mass. "

The "...regardless of its mass" statement seems counter-intuitive to me. What if that planet turned out to be a super-giant red star much greater in mass than the Sun? Then the Sun would orbit the red star right? How can the red star still have an orbital period of 5.2 years? Thank you.
 
The "...regardless of its mass" statement needs to be taken in the context of the basic assumption of Kepler's Laws where the masses of all the planets are considered to be much less than that of the primary (the Sun).

So I guess one might say that the mass of the object doesn't matter as long as it is insignificant :smile:
 
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gneill said:
The "...regardless of its mass" statement needs to be taken in the context of the basic assumption of Kepler's Laws where the masses of all the planets are considered to be much less than that of the primary (the Sun).

So I guess one might say that the mass of the object doesn't matter as long as it is insignificant :smile:
Thank you
 

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